13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Crack growth stability analysis with respect to boundary disturbance Hao Chen1,* 1 Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, CEA, Sanhe, 065201, China * Corresponding author: chenhao@iem.ac.cn Abstract Fracture analysis is a high non-linear problem and affected by uncertainties. Because of the limitation of observing technology, accuracy boundary condition can hardly be obtained. Normally, a stochastic model can be used. The difference between reality and numerical model is deemed as disturbance. This paper presents a three-dimension dynamic stability analysis of crack growth under disturbance in boundary condition by using particle discretization scheme finite element method. The model is a thin epoxy plate with two anti-symmetric notches located in the middle, under uni-axial tensile in longitudinal direction. Two types of disturbance are considered: (i), the disturbance is added to the initial cracks’ configuration. The disturbance is modeled by adjusting the position, size and shape of the notches. It shows that changes of the notches’ size and position have significant influence on crack growth in the investigated cases; (ii), the disturbance is applied to the displacement boundary condition, which is far from initial cracks. The variability of crack paths of different model sizes under the same disturbance is estimated. The results of the numerical experiment indicate that as the model size increases, the influence of the disturbance becomes weaker. The Saint-Venant principle still holds in the studied crack growth problem. Keywords Three dimensional dynamic crack growth, particle discretization scheme, finite element method, boundary disturbance, stability analysis 1. Introduction Fracture analysis is a hot topic in solid mechanics [1]. Both experiments [2] and numerical methods have been developed to investigate the fracture behavior. The physical experiment is a reliable way. However, it costs a lot of resources to conduct. As the accumulation of experimental data increases, the fracture mechanics of more and more materials can be studied by using numerical method, for its convenience and resources saving. In order to increase the reliability of simulation results, a numerical model needs to be built as accurately as possible. However, the current observation equipments and technology have their limitation. Therefore, differences between reality and numerical model exist. Normally, stochastic model can be proposed, and the average value with variances can be used in numerical simulation. The difference between reality and numerical setting is deemed as disturbance in this paper. Since the crack drastically changes the stiffness matrix and strain energy, the dynamic crack propagation becomes a high non-linear problem. Hence, the results may be affected by these uncertainties. In mathematical view point, instability means that when a small perturbation is added to a system, the results will drastically change. This paper focuses on studying the effect of the boundary condition disturbance on an elastic dynamic fracture problem. The well known Saint-Venant principle tells that, as the distance between the target and disturbance source increases, the effect of the disturbance decreases. Meanwhile, Oguni et al. [3] states that for dynamic fracture stability analysis, the uncertainties can be deemed as disturbance added to the stiffness matrix. As time increases, the effect may be increased or maintained according to system property. Based on these two theories, for boundary disturbance problems, it can be inferred that the effect of disturbance in boundary condition fades as the distance from area of interest increases, and heightens or maintains as time increases. However, since the property of dynamic fracture problem is nonlinear, the effects need to be quantificationally estimated.
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